In the previous chapter I argued that Dummett’s intermediate position on abstract entities is compromised by his failure to articulate a more thoroughgoing account of what a ‘thin’ notion of reference for abstract singular terms consists in. The burden placed on such an account is to provide an explanation of how abstract singular terms can be ascribed a reference whilst also acknowledging the relevant disanalogies with the more robust notion of reference applicable in the case of names for concrete objects. Insofar as Dummett vacillates on the possibility of ascribing abstract singular terms a semantic role and only gives a fragmentary account of what a ‘thin’ notion of reference consists in, his position is vulnerable to the criticism of Wright and Hale that there can be no intermediate position on abstract objects. In the current section I will attempt to supplement Dummett’s account of tolerant reductionism by looking at recent work by Øystein Linnebo – which has been endorsed by Dummett — on ‘thin’ theories of reference for mathematical terms.
KeywordsAbstract Object Mathematical Object Singular Term Ontological Commitment Concrete Object
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